Stability study of the higher order mode beam position monitors at the Accelerating cavities at FLASH

When electron beams traverse an accelerating structure, higher order modes (HOMs) are excited. They can be used for beam diagnostic purposes. Both 1.3 GHz and 3.9 GHz superconducting accel erating cavities at FLASH linac, DESY, are equipped with electronics for beam position monitoring, which are based on HOM signals from special couplers. These monitors provide the beam position without additional vacuum components and at low cost. Moreover, they can be used to align the beam in the cavities to reduce the HOM effects on the beam. However, the HOMBPM (Higher Order Mode based Beam Position Monitor) shows an instability problem over time. In this paper, we will present the status of studies on this issue. Several methods are utilized to calibrate the HOMBPMs. These methods include DLR (Direct Linear Regression), and SVD (Singular Value Decomposition). We found that SVD generally is more suitable for HOMBPM calibration. We focus on the HOMBPMs at 1.3 GHz cavities. Techniques developed here are applicable to 3.9 GHz modules. The work will pave the way for HOMBPMs of the E-XFEL (European X-ray Free Electron Laser).